On conditions determining formal automorphisms of integro-differential operators

2023/06/10 by Lastra, Alberto, Michalik, Sławomir, Suwińska, Maria · 1 citation
#35C10 #35G10 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.06398

Abstract

Results providing conditions on a family of integro-differential operators to determine a formal automorphism are established. Equivalently, the problem can be read in terms of existence and uniqueness of formal solutions of Cauchy problems in different settings. The main achievements provide a three-statement result not only in the framework of general formal power series, but also on subspaces appearing in applications such as Gevrey settings and moment differential operators.

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